Could Game Theoretic Price Collusion be Legal?

Price fixing or price collusion occurs when companies agree to keep the price of a product or service at an elevated level (or limit production) with the goal of receiving large profits or cornering the market. This is deemed illegal. I am wondering whether price fixing could be legal if it is the result of so-called repeated or iterated games.

Let us make some assumptions. These may be relaxed later – it would not greatly change the conclusions. Let us assume a market of two companies. The market has significant entry barriers, which means that new companies cannot (quickly) enter. Now, assume that the following profit matrix holds:

Company A
low high
Company B low 1 /1 -1 / 5
high -1 / 5 3 / 3

If both companies keep prices at a “high” level, they could both earn 3. If one company decides to lower prices, it can earn 5. The other company, if it would not simultaneously lower prices as well, would then suffer a loss of 1. If one company lowers prices, the other has to respond by lowering prices as well, otherwise it would eventually have to go out of business.

If companies A and B would have contact, and agree to keep prices high, then they would be breaking the law – this would be price collusion. But let us assume that the two companies do not have any contact whatsoever. Does it then automatically follow that prices will be lowered?

I would say, no. If we think of this market situation in a framework of repeated games, both companies could realise that if they would lower prices and elicit a price war, they would both lose. If one company lowers prices, it will expect to be punished by its competitor. They might thus reason something like the following: If I keep prices high, it might be the case that the other company keeps them high as well, which would give us both a decent profit. But even if my competitor lowers his prices, I can punish him by lowering mine in the next round. If both companies reason like this, it becomes clear that a situation of high prices is reached, without any explicit price collusion.

This seems to be evidenced by the results of Axelrod’s tournaments. Robert Axelrod, an American political scientist, organised an experiment where numerous game theoretic strategies where paired, to see which one would be most successful if all games were aggregated. The winning and most successful strategy was a “tit for tat” strategy: be nice to your competitor, but if he is not nice to you, you respond with being not nice. This corresponds quite accurately to the sketched situation above, where “being nice” corresponds to “keeping prices high”.

So now I wonder, if companies would manage to “fix” prices not so much by explicit fraudulent price agreements, but by reaching a game theoretic equilibrium, would this be considered illegal or not?


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